Plots results from correspondence analysis or multiple correspondence analysis (A.I. Glaser).

### Options

`DIMENSIONS` = scalars |
Two numbers specifying which axes of the ordinations to plot; default 1,2 |
---|---|

`PLOT` = string tokens |
Which scores to plot (`rowscores` , `rowactive` , `rowpassive` , `colscores` , `colactive` , `colpassive` ); default `rows` , `cols` for correspondence analysis and `cols` for multiple correspondence analysis |

`ROWSCALING` = string token |
Scaling to use for row coordinates (`principal` , `standard` , `mass` , `sqrtmass` ); default `prin` |

`COLSCALING` = string token |
Scaling to use for column coordinates (`principal` , `standard` , `mass` , `sqrtmass` ); default `prin` |

`COLOURMETHOD` = string tokens |
Whether colour of symbol should show level of inertia of rows or columns (`rowinertia` , `colinertia` ); default `*` |

`SIZEMETHOD` = string tokens |
Whether size of symbol should show row or column masses (`rowmass` , `colmass` ); default `*` |

`FACCOLOURS` = text, variate or scalar |
Specifies a colour or colours for the factors in a multiple correspondence analysis; if this is unset, a different colour is selected automatically for every factor |

`WINDOW` = scalar |
Which graphical window to use; default 1 |

`KEYWINDOW` = scalar |
Graphical window for the key |

`SAVE` = pointer |
Supplies results from a analysis by `CORANALYSIS` or `MCORANALYSIS` ; default uses the most recent analysis |

### Parameters

`TITLE` = texts |
Titles for the plot |
---|---|

`LMROWVARIABLES` = string tokens |
How to label the row scores (`identifiers` , `labels` , `none` , `numbers` ); default `labe` if `LROWVARIABLES` is set, otherwise `iden` |

`LMCOLVARIABLES` = string tokens |
How to label the column scores (`identifiers` , `labels` , `none` , `numbers` ); default `labe` if `LCOLVARIABLES` is set, otherwise `iden` |

`LROWVARIABLES` = texts |
Labels for row variables |

`LCOLVARIABLES` = texts |
Labels for column variables |

### Description

`CABIPLOT`

provides a graphical representation of results from `CORANALYSIS`

or `MCORANALYSIS`

. By default `CABIPLOT`

plots both sets of scores (rowscores, colscores) for correspondence analysis or just columns scores for multiple correspondence analysis, but you can set option `PLOT`

to select which ones are required. For correspondence analysis, you can also select settings that will plot only active or passive scores (see `CORANALYSIS`

for further explanation).

The row scores are plotted as blue circles, while the column scores are plotted as red squares; active scores have filled symbols, but passive scores are not filled. With multiple correspondence analysis, the `FACCOLOURS`

option can be used to define the colour to use for each factor, using either RGB values (in a variate or scalar) or the standard Genstat colour names (in a text); see `PEN`

for more details. If insufficient colours are specified, `CABIPLOT`

will recycle the list. So you can set `FACCOLOURS`

to a scalar or to a text with a single string if you want to use the same colour for all the factors. If `FACCOLOURS`

is not set, `CABIPLOT`

will select a different colour for each factor automatically.

The `ROWSCALING`

and `COLSCALING`

options are define the scaling to use for the row and columns coordinates respectively, with settings:

`principal` |
plots principal coordinates (default), |
---|---|

`standard` |
plots standard coordinates, |

`mass` |
plots standard coordinates multiplied by the row (or column) mass, |

`sqrtmass` |
plots standard coordinates multiplied by the square root of the row (or column) mass. |

These are based on the row and column scores obtained from `CORANALYSIS`

or `MCORANALYSIS`

. Principal coordinates are scaled so that they have inertia equal to the square of the singular values, whereas the weighted sum-of-squares of the standard coordinates are equal to one. At least one of `ROWSCALING`

or `COLSCALING`

must be set to `principal`

, which is the default for both options. These default settings produce a plot, which is not a biplot, but which is used very often to illustrate relationships between and amongst variables. The reasoning behind multiplying the standard coordinates by the corresponding mass or its square root is to “pull” the rarer categories to be closer to the origin; see Chapter 13 of Greenacre (2007).

The `COLOURMETHOD`

option has settings `rowinertia`

and `colinertia`

that plot the row or coordinates scores, respectively, at a different level of shading; the coordinates with higher inertias are plotted with darker colours then those with low inertias. The shading is proportional to the square root of the inertia relative to the row or column with the highest inertia. Symbols representing passive points will appear completely transparent on the plot as they are perceived to have zero inertia.

The `SIZEMETHOD`

option similarly has settings `rowmass`

and `colmass`

that plot the row and column coordinates, respectively, in sizes that depend on the row and column mass. The sizes of the symbols are proportional to the square root of the mass compared to the square root of the row or column with the highest mass, plus a constant to ensure all symbols are visible.

By default the first two dimensions are plotted, but you can specify other dimensions to be plotted using the `DIMENSIONS`

option.

The data used in `MCORANALYSIS`

may have many repeated values (particularly in survey data). To avoid replotting the same points in a large data set (i.e. with more than 500 units), only one point is plotted and the label refers to the first point in the data set. If the `COLOURMETHOD`

or `SIZEMETHOD`

options are set, these will use the mass and/or inertia of the labelled point.

The labels for the row and column scores can be set using the `LMROWVARIABLES`

and `LMCOLVARIABLES`

parameters, by selecting one of the following settings:

`identifiers` |
uses the identifiers of the row or column scores, |
---|---|

`labels` |
expects labels to be supplied (in a text) using the `LROWVARIABLES` or `LCOLVARIABLES` parameter, |

`none` |
gives no labels, and |

`numbers` |
uses the row or column numbers of the original matrix. |

The default for both parameters is `identifiers`

, unless `LROWVARIABLES`

or `LCOLVARIABLES`

is set, when the corresponding default becomes `labels`

. Note that the texts supplied by `LROWVARIABLES`

or `LCOLVARIABLES`

must have the same number of values as number of the rows or columns in the original data matrix, even if active or passive points are being omitted from the plot. Similarly, if the setting `numbers`

is chosen, these will refer to the corresponding row or column of the original matrix, ignoring any any active or passive rows or columns, or subsetting of rows or columns in `CORANALYSIS`

.

By default `CABIPLOT`

uses the results from the most recent analysis from by `CORANALYSIS`

or `MCORANALYSIS`

. However, you can display results from an earlier analysis by saving the information about the analysis with the `SAVE`

parameter of `CORANALYSIS`

or `MCORANALYSIS`

, and then using this as the setting of the `SAVE`

option of `CABIPLOT`

.

Options: `DIMENSIONS`

, `PLOT`

, `ROWSCALING`

, `COLSCALING`

, `COLOURMETHOD`

, `SIZEMETHOD`

, `FACCOLOURS`

, `WINDOW`

, `KEYWINDOW`

, `SAVE`

.

Parameters: `TITLE`

, `LMROWVARIABLES`

, `LMCOLVARIABLES`

, `LROWVARIABLES`

, `LCOLVARIABLES`

.

### Method

The plots are explained in Chapter 13 and 18 of Greenacre (2007).

### Reference

Greenacre, M. (2007). *Correspondence Analysis in Practice, second edition*. Chapman & Hall, London.

### See also

Procedures: `CORANALYSIS`

, `MCORANALYSIS`

.

Commands for: Multivariate and cluster analysis, Graphics.

### Example

CAPTION 'CABIPLOT examples',!t('1) Correspondence analysis:',\ 'biplot for smoking data from Table 3.1 of Greenacre (1984)';\ STYLE=meta,minor TEXT Staff; VALUES=!T(Sen_Mngr,Jun_Mngr,Sen_Empl,Jun_Empl,Secretary) & Smoke; VALUES=!T(None,Light,Medium,Heavy) MATRIX [ROWS=Staff; COLUMNS=Smoke; VALUES=\ 4,2,3,2, 4,3,7,4, 25,10,12,4, 18,24,33,13, 10,6,7,2] Smoking CORANALYSIS Smoking CABIPLOT CAPTION !t('2) Multiple correspondence analysis:',\ 'Exhibit 18.2 (p. 139) from Greenacre (2007)'); STYLE=minor " The data come from an International Social Survey Programme (ISSP) survey of Family and Changing Gender Roles in 1994 in 24 countries. The spreadsheet MCOR-1.gsh contains the opinions of German residents about working women for 4 questions, each with 4 possible responses." SPLOAD FILE='%gendir%/examples/MCOR-1.GSH' POINTER [VALUES=Q1,Q2,Q3,Q4] women MCORANALYSIS [COLMETHOD=indicator] women CABIPLOT [PLOT=colscores]